Yes it will likely affect the rankings of your site. When Google finds duplicated content it must make a decision as to which page is the original. Amazon.com is one of the most authoritative web sites on the internet right now, therefore Google would likely pick Amazon over any other site when there is duplicated content.

If you want to rank both websites on SERPs, you need to change your product descriptions a bit. They should be unique because like what JoeHall mentioned, Google will detect this and will only rank one site (based from which whoever is original and whoever has good reputation online).